But, it is quites possible that
Avonex would also be okay for you.
Avonex is a far lower dose per week, and since you have already acheived the immune response with the Rebif would kick in quickly. But, if you are very sensitive to the side effects of the Rebif, you might have them also with the Avonex.
Now this is based on what I have read and NOT on experience. I am actually pretty ignorant of how these meds react in different people. But, these are my thought anyway.